Hardy Fields and Applications to Symbolic Asymptotics
by
John Shackell
University of Kent at Canterbury

One might think of Hardy fields as ordered fields of functions where the order reflects the asymptotic behaviour. This order makes Hardy fields an excellent tool in asymptotics.

For many purposes, it is useful to consider certain partial orders which are derived from the Hardy-field order, but are coarser. One such is the valuation. Others, such as the rank, may be obtained by applying the valuation to iterated logarithms of elements. These orders can yield important information concerning various sorts of asymptotic expansions.

For Hardy fields of finite rank, results and their application to asymptotics go back several years. However more recent research shows that information can also be obtained in the infinite-rank case. Here an important role is played by the direct limit of the orders obtained from the iterated logarithms.

Date received: April 30, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacv-43.